Prove the following trigonometric identities
`cos^2 A + 1/(1 + cos^2 A) = 1`
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Solution
We know that
`sin^2 A + cos^2 A = 1`
`cosec^2 A - cot^2 A = 1`
So,
`cos^2 A + 1/(1 + cot^2 A) = cos^2 A + 1/(cosec A)`
`= cos^2 A + (1/cosecA)^2`
`= cos^2 A + (sin A)^2`
`= cos^2 A + sin^2 A`
= 1
Concept: Trigonometric Identities
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